Book/Report

FZJ-2018-04521

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Chance and chaos in seasonally driven epidemics

Engbert, R. (Corresponding author)FZJ*

1993
Forschungszentrum Jülich GmbH Zentralbibliothek Verlag Jülich

Please use a persistent id in citations: http://hdl.handle.net/2128/19437

Report No.: Juel-2826

Abstract: In spite of their complex behaviour the dynamics of some ecological systems may be explained by deterministic laws of motion. This is clearly theoretically possible, because deductive approaches to the dynamics of ecological systems lead to nonlinear models and even very simple model ecosystems generate typically a rich spectrum of dynamics, ranging from coexisting periodic regimes to chaotic behaviour. The search for chaos in ecology has drawn much attention to the analysis of recurrent outbreaks of childhood epidemics - in particular of measles infections - in large population centers. Because of the public interest in controlling outbreaks, the incidence of infectious diseases has long been registered. As a result, the corresponding time series are quite long compared to other ecological systems (about 30 years in the pre-vaccination period). Furthermore the number of inhabitants of large population centers (~ 10$^{6}$ to 10$^{7}$) seems to be high enough to enable the separation nonlinear determinism from stochastic fluctuations. This work is intended to analyse the complex interplay between deterministic nonlineardynamics and demographic stochasticity in a class of epidemiological models. My analysis lends support to the plausibility of chaos. In a situation of transient chaos stochastic perturbations may generate chaotic dynamics, inspite of the fact that the unperturbed asymptotic behaviour is periodic. However, for decreasing population size (increasing fluctuations) the distinction between chaos and stochasticity becomes more and more problematic. The problem of immigration of infectives into the host population is discussed. A modification of the standard epidemiological model is proposed in order to analyse the effects of a coupling between different cities. This modification results in a better agreement with models obtained by nonlinear time series analysis. The methods of analysis being used here may prove to be helpful in understanding other fluctuating systems in ecology (and epidemiology). The interplay between deterministic dynamics and stochastic fluctuations, e. g. due to the integer structure of populations or a noisy environment, suggests an analysis combining methods from the theory of nonlinear dynamical systems as well as stochastic processes.

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Contributing Institute(s):

1. Publikationen vor 2000 (PRE-2000)

Research Program(s):

1. 899 - ohne Topic (POF3-899) (POF3-899)

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Database coverage:

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